I doubt it. We would have to amend the constitution, because he was not born a U.S. citizen. Amending the constitution is extremely difficult, requiring 2/3 passage in the House and Senate and ratification by 2/3 of the states. Assuming this happened, which would likely take years, Arnold would still need to be relevant. After he leaves the Governor's office his star will fade, unless he becomes a senator or something.
Then his timing would have to be good (e.g., he cannot run against an incumbent Republican president).
I don't see it happening.